1. Field of the Invention
The present invention relates generally to a loudspeaker, and, more particularly, to a loudspeaker having a diaphragm of novel construction.
2. Description of the Prior Art
In general, a speaker unit has an electro-mechanical converter, for example, a voice coil driven by an electrical input signal, to vibrate a diaphragm which is connected to the voice coil. In order to maintain a relationship between sound pressure and frequency, that is, the sound-pressure/frequency characteristic, it is necessary that the speaker be driven within a limited so-called piston vibration region. That is, if the speaker is driven at a frequency higher than the critical value of the piston vibration region, a so-called divided vibration is produced, whereby the sound quality is deteriorated. For this reason, in order to improve the sound-pressure/frequency characteristic of a speaker unit, the prior art has attempted to increase the critical value of the piston vibration region. The problem of divided vibration will be described with respect to a plane diaphragm (e.g. vibrating plate).
In the phenomenon of divided vibration, there are various kinds of vibration modes; and the frequencies at which the respective modes of divided vibrations occur are different and are dependent upon the particular vibration modes. For example, if the plane diaphragm is circular, the frequency f.sub.nm at which each mode of divided vibration occurs is expressed as: ##EQU2## where a is the radius of the circular vibrating diaphragm, D is the flexural rigidity of the vibrating diaphragm, .sigma. is its surface density of the diaphragm and .lambda..sup.2 nm is a factor of the (n, m) mode. If n=0, then the (0,m)mode (m = 0, 1, 2 . . . ) is a divided vibration which is present in a prior art coneshaped diaphragm.
As may be apparent from equation (1), the divided vibration frequency f.sub.nm will be high if the flexural ridigity D of the diaphragmn is large and/or if the radius a and/or the surface density .sigma. of the diaphragm are small. However, the radius a usually is preselected in accordance with other considerations to be a desired value. Accordingly, the critical value of the divided vibration frequency of the diaphragm is determined primarily by its flexural rigidity and surface density .sigma..
Now, a plane plate of isotropic material will be considered. The flexural rigidity D and surface density of the plate may be expressed as: ##EQU3## where E is the longitudinal elastic modulus of the material of which the plate is constructed, .nu. is Poisson's ratio, t is the thickness of the plate and .rho. is its volume density. From equation (2), the term D/.sigma. in the right side of equation (1) can be expressed as follows: ##EQU4## Since the poisson's ratio .nu. is within a range of 0.1 to 0.5, it has only a minimal effect on the term D/.sigma..
A typical speaker having a plane plate type diaphragm is made of beryllium, for example. Beryllium is known to have the highest .sup.E /.rho. factor. One type of speaker unit has a diameter of 30cm, and the effective diameter of the diaphragm thereof is 24cm. If the diaphragm is formed as a disc having a diameter of 24cm, its mass may be selected to be 30g (for the purpose of efficiency), its surface density .sigma. may be selected to be 0.663 kg/cm.sup. 2 and its thickness may be selected to be 0.36 mm (with Poisson's ratio .nu. equal to 0.3). From equation (1), the frequency f.sub.2,0 at which lowest (2, 0) mode in the divided vibration appears is calculated to be f.sub.2.0 = 77.1 H.sub.z. This low value of the divided vibration frequency means that the critical value of the piston vibration is 77.1 H.sub.z, thus making such a speaker unit impractical. In order to drive the diaphragm, a voice coi and associated means must be attached to the diaphragm, and their cumulative mass affects the divided vibration frequency value, so that the frequency is further decreased. Accordingly, it is appreciated that a general plane plate of isotropic material will not perform satisfactorily as a speaker unit.
In view of the foregoing, a complex diaghragm has been proposed wherein a layer of aluminum alloy is secured to opposing surfaces of a core made of styrene foam. As a practical example, an aluminum alloy film having a thickness of 30.mu. (micron) is employed as the layer and styrene foam having a thickness of 12 mm is used as the core. The effective diameter of the diaphragm is selected to be 24 cm, the mass of the diaphragm (including a mass of 9.sub.g of the adhesive agent) is selected to be 29.1g, and the mass of the voice coil is selected to be 7.5.sub.g. The density .rho.f of each layer is 2690 kg/m.sup.3, the density .rho. c of the core is 23.5 Kg/m.sup.3, the longitudinal elastic modulus E.sub.f of each layer is 7 .times. 10.sup.10 N/M.sup.2, and the shearing elastic modulus G.sub.c of the core is 3.5 .times. 10.sup.6 N/m.sup.2. The equivalent flexural rigidity D of this complex diaphragm, formed as a plate with a beam taken as l, is expressed by the equation below. In this example, the thickness t.sub.f of the layers on both surfaces of the core is assumed to be equal.
When the complex diaphragm is made by sandwiching a core between two layers, and a pressure P is applied to this diaphragm from one layer, the distortion factor .delta..sub.s of the layer is expressed as: ##EQU5## and the distortion factor .delta..sub.c of the core is expressed as: ##EQU6## where P is the applied pressure, l is the length of the beam, t.sub.f the thickness of a layer, t.sub.c is the thickness of the core, t is the thickness of the complex plate (equal to 2t.sub.f +t.sub.c), b is the width of the diaphragm, E.sub.f is the longitudinal elastic modulus of a layer, and G.sub.c is the shearing elastic modulus of the core.
For a simple diaphragm, its distortion factor .delta. is expressed as: ##EQU7## where D is the flexural rigidity of the diaphragm.
If the following equivalency is established, EQU .delta. = .delta..sub.s + .delta..sub.c
then the equivalent flexural rigidity D is approximately: ##EQU8##
The surface density .sigma. for this complex diaphragm may be EQU .sigma. = .rho..sub.c t.sub.c + 2 .rho..sub.f t.sub.f ( 5)
where, it is recalled .rho..sub.c is the density of the core and .rho..sub.f is the density of each layer.
Accordingly, the equivalent flexural rigidity of this complex diaphragm of the prior art, in which the core is made of styrene foam and each layer is made of aluminum alloy, is derived from equation (4) to be 60.9N.m (the shearing elastic modulus G.sub.c of the core being 3.5 .times. 10.sup.6 N/cm.sup.2). Thus, if the equivalent flexural rigidity D calculated from equation (4) and the surface density .sigma. calculated from equation (5) are substituted into the equation (1), the divided vibration frequencies are calculated to be f.sub.0,1 .apprxeq.680H.sub.z and f.sub.0,2 .apprxeq. 1.8 KH.sub.z, respectively.
The critical value of the piston vibration region obtained by the prior art complex diaphragm plate is about 680 H.sub.z. Although this is an improvement over the region obtained by a cone speaker of the same size, the value still is not satisfactory. One of the reasons for the limitation on the piston vibration region is that the shearing elastic modulus G.sub.c of the core is considerably low.
Another example of a vibrating plate diaphragm used in a board-speaker, is a complex diaphragm in which two paper liners sandwich a honey-comb core between them (for example, laid-open Japanese Patent Application No. 64417/1974). This complex diaphragm may be considered to be a vibrating plate which is used in a panel-type speaker in which the tablet of the panel, which may be ornamental or may have a picture or photograph also is the vibrating plate. In this example, the density .rho..sub.f of the paper liner having a thickness of 0.1 mm is 800 Kg/m.sup.3 and the density of the honey-comb core having a thickness of 12 mm is 25.6 Kg/m.sup.3. The longitudinal elastic modulus E.sub.f of the paper liner is 3 .times. 10.sup.9 N/m.sup.2 and the shearing elastic modulus G.sub.c of the honey-comb core is 4.1 .times. 10.sup.7 N/m.sup.2. If the other parameters, such as length l, are to be substantially the same as those mentioned above in the foregoing example, then the divided vibration frequencies are calculated from equations (1), (4) and (5) to be f.sub.0,1 .apprxeq. 435 H.sub.z and f.sub.0,2 .apprxeq. 1.1 KH.sub.z, respectively.
The acoustic qualities of the above prior art complex diaphragms, with respect to various characteristics such as frequency characteristic, directional characteristic and the like, are less than satisfactory, and can be significantly improved.